Import Question JSON

Current Question (ID: 16825)

Question:

$\text{The two parts of the loop are circles of radii } 2a \text{ and } a, \text{ respectively, and carry the same current } i \text{ as shown in the given figure. What is the magnitude of the dipole moment of the current loop?}$

Options:

1. $5\pi a^2 \hat{i}$
2. $4\pi a^2 \hat{i}$
3. $3\pi a^2 \hat{i}$
4. $\text{zero}$

Solution:

$\text{Hint: } M = I \times A$ $\text{Step 1: Find the magnetic moment for individual loops.}$ $\text{The magnetic moment for individual loops is given by:}$ $\vec{M}_1 = i\pi (2a)^2$ $\vec{M}_1 = 4\pi a^2 i \odot$ $\vec{M}_2 = i (\pi a^2)$ $\vec{M}_2 = \pi a^2 i \otimes$ $\text{Step 2: Find the net magnetic moment.}$ $\text{The net magnetic moment is given by:}$ $\vec{M}_N = \vec{M}_1 + \vec{M}_2$ $\vec{M}_N = 4\pi a^2 i - \pi a^2 i$ $\Rightarrow \vec{M}_N = 3\pi a^2 i$ $\text{Hence, option (3) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}